Mean dimension of full shifts

2017/12/08 by Tsukamoto, Masaki · 4 citations
#37B99 #54F45 #Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1712.03050

Abstract

Let K be a finite dimensional compact metric space and K^ℤ the full shift on the alphabet K. We prove that its mean dimension is given by dim K or dim K-1 depending on the "type" of K. We propose a problem which seems interesting from the view point of infinite dimensional topology.

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• Relative topological entropy and relative mean dimension of induced factors
• Explicit formulae and topological descriptions of action-minimizing sets of a full shift with an uncountable alphabet [0,1]
• Dynamical dimension and shift embeddability without the marker property

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